text:
How useful are the AOA Indexers and indicators for jet pilots and civillians?
I dont see them neccessary unless you are landing on a aircraft carrier.
I just don't know a lot about them. I understand what they do but they just dont seem neccessary unless you are landing a jet to an aircraft carrier where every bit of precise information is neccessary.
And now I see them on the Cessna 172SP planes.
Long story short. How important they are for aircraft carrier pilots and Cessna students/pilots?

They can be useful, think about in a level turn, the aoa indicator will tell you how close you are to a stall when additional loading changes your stall speed.

Gyroscopic-instruments tag ought to be removed

They’re super useful once you get used to them. No matter your weight, if you fly at the right AOA you’ll have the right stall margin. It is easier to see the indexer than the ASI, for control on approach. It acts like a pitch rate indicator too, if you are rough with the nose, so it helps to smooth out the flying. Responds much faster than the ASI. If you are maneuvering aggressively, it will give you that stall margin too.
Update with nice paper from AIAA Journal of Aircraft:
"Low-Cost Accurate Angle-of-Attack System", Borja Martos and David F. Rogers, Journal of Aircraft 2018 55:2, 660-665

...The angle
  of attack for maximum lift-to-drag ratio corresponds to maximum range
  and maximum glide ratio for a piston engine- propeller aircraft.
  Hence, in a fuel critical situation and/or an engine failure
  situation, it is critical that the pilot have accurate access to this
  angle of attack.
With today’s fuel costs, the Carson cruise [1] angle of attack, which
  represents the most efficient way to fly fast with the least increase
  in fuel consumption, is of significant interest.
The angle of attack for maximum lift-to-drag ratio does not depend on
  density altitude, weight, or load factor but only on aircraft design
  parameters and aircraft configuration. Similarly, the angles of attack
  for minimum power required and Carson cruise depend only on aircraft
  design parameters and configuration...
Therefore, a low-cost, accurate, full envelope, easy to flight
  calibrate angle-of-attack system is a transformative technology for
  light general aviation aircraft.

Hi Mike!  I just posted a question that it might interest you to answer, based on your answer to this one.

Accidental stalls are fairly common, especially for new pilots, and that's why we have stall warning devices--and train pilots to immediately recover as soon as they hear/see them.  However, simple devices don't tell you anything until you're right on the edge.  For more complete information, you need an AOA sensor.  Once you have that sensor, why not display that information to the pilot?  If you have a glass cockpit, the cost of adding one more data item on the display is pretty much zero, and it might be useful to some pilots--regardless of whether they're flying a trainer, an airliner, or a fighter.

Planes that fly off aircraft carriers rely on them heavily.  They not only have indexer lights in the cockpit, but they also have them on the outside of the plane (usually on the nose gear doors) so the Landing Signals Officer on the boat can see them as well.  Depending on the aircraft, they might not even turn on unless the landing gear is down, because they're calibrated for approach speeds.
On the planes I'm more familiar with, we rarely use it at all because it's a real pain to calibrate.  We also have two independent pitot-static systems, so a loss of all airspeed indications is a remote (but not impossible) scenario.

On the F18 they are in fact attached to the nose landing gear. So no gear down = no lights visible.


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What is the relationship between Angle of Attack and Angle of Incidence?
The Angle of Incidence (AoI) of most GA planes is 6°. Assuming a plane with an Angle of Incidence of 6 degrees--
How do we calculate pitch attitude if we know the direction of the flight path and the Angle of Attack?  This is essentially a question about whether Angle of Attack is measured in relation to the chord line of the wing, or in relation to the longitudinal axis of the fuselage.
During takeoff, the Angle of Attack (AoA) is often 11° or more.  Is the 11° AoA measured in relation to the chord line of the wing, so that the pitch attitude at takeoff is 11 - 6 = 5 degrees?

This question is unclear.  Do you know the angle-of-attack, or don't you?  It seems you do.  So know the angle-of-attack, and the angle-of-incidence, and you are asking how to calculate the pitch attitude?  Basically it sounds like you are saying "I know the angle-of-attack but I don't know what it means and therefore I'm not sure how to calculate the pitch attitude from it."  Is that right?  If not, you could improve the question.

@quietflyer If you think the question is unclear and it should be closed, why did you answer?

@Bianfable well, you do the best you can to clear up the confusion of the asker.  Who knows whether the question will actually be closed, and others may be led astray whether it is closed or not.  If I've violated ASE etiquette in some way, let me know, and I'd appreciate a link to a page that spells out what I did wrong.  Just out of curiosity, is there a way to see who submitted a close vote, or did you just make the logical assumption based on the fact that I commented?

Specifically, to try to be more constructive about improvements-- "does the 11° AoA include the initial 6° AoI in it i.e, 11 - 6 = 5"-- what is exactly is the thing that you are suggesting may be equal to 5?  Pitch attitude, or something else?  "does the 11° AoA include the initial 6° AoI in it i.e, 11 - 6 = 5?  Meaning the deflection for takeoff will be 5° (plus 6° of incidence)?"  What exactly is the thing that you are calling "deflection"?  Pitch attitude. or something else?

(Ctd) ""when I say my plane is climbing with an AoA of 11°, does this 11° include the wings' AoI?" -- in exactly what calculation are you asking whether or not AoI should be "included"?  Calculation of pitch attitude starting from Angle of Attack?  Or some other calculation?

@quietflyer No, I cannot see that you voted to close, only if you had done it via review, but I assumed based on your comment. I don't think it is a violation of any rule, it just seems weird to me.

Yes it's a little weird...

Of course someone could always improve it, if they were sure enough of the original intent of the asker, which seems fairly clear.

(Comments ctd)-- "What I am asking is, when I say my plane is climbing with an AoA of 11°, does this 11° include the wings' AoI?"  since you haven't specified the climb angle, this part of the question seems meaningless.  What would you be trying to calculate using the 11 degrees figure, without knowing the climb angle?

@Bianfable -- substantial edit to try to best express what the original asker was trying to get at it-- I'll retract the close vote if edit does not get rolled back.  Unclear to me whether I would be allowed to re-cast it I retracted it now and then edit were rolled back.

Not a duplicate of "https://aviation.stackexchange.com/questions/56475/what-is-the-difference-between-angle-of-incidence-aoi-and-angle-of-attack-aoa" because that question is really asking about whether we consider propwash effects etc in considering the direction of the relative wind.

Speaking of an aircraft, the AOA is simply the angle between the airflow and the aircraft fuselage, in the vertical plane.
The incidence is only required to calculate the wing AOA. The wing AOA is the sum of AOI and AOA_aircraft.
When talking to some aerodynamicist or another engineer, it’s a good practice to state your conventions the first time you use a term, to avoid miscommunication.

Not really.
The angle of incidence is the angle between the chord of the wing and the longitudinal axis of the airplane.  But the plane is mostly free to pitch as necessary.  So if the best thing is for the wing to have an AOA of 11°, then it can pitch to that point.
Now if the angle of incidence were too different, it could increase drag on the climb-out, or the thrust angle might be less than optimal.  But there's no direct relationship.
The angle of incidence is a figure about the geometry of the plane.  The angle of attack is how the wing is oriented to the wind.  They don't "add" together.
If you did the math the other way (AOA - AOI), you'd find the angle the wind is making with respect to the airplane axis, not a figure that you tend to need.

So if I understand correctly,aoa is totally independent of the angle of incidence?

Simpler question: what is the angle between chord of wing and the ground when the plane has AOA of 11°? 11° or 17°?

@SF Not a simple relation.   Angle to ground depends only on attitude (pitch).  AOA depends on path through the air.  It would be different for a climbing vs descending plane.

@DavidTeahay I hate to say "totally independent", but yes that's right.  The angle of incidence is completely fixed while you're flying.  The AOA is quite variable as you adjust attitude and path through the air.

@SF But if the plane is flying level and the air is still, then the AOA and the wing angle to ground are identical.

@BowlOfRed: Oh. This is what I wanted to know. It's the wing angle, not hull angle.

"So if the best thing is for the wing to have an AOA of 11°, then it can pitch to that point." --did you possibly mean "if the pilot is holding the elevator in the position that commands an AoA of 11 degrees, then the plane can pitch to that point", or something like that?

What they all said, just basically Angle of Attack is created by the pilot pitching the airplane, Angle of Incidence is set by the manufacturer, cannot be adjusted.

The asker seemed clear on what Angle of Incidence was and also seemed clear that Angle of Attack would vary if the pilot changed the elevator deflection.

During takeoff, the Angle of Attack (AoA) is often 11° or more. Is the
  11° AoA measured in relation to the chord line of the wing, so that
  the pitch attitude at takeoff is 11 - 6 = 5 degrees?

It seems odd that a pilot would know his plane's angle-of-attack in a given situation, but not know what the angle-of-attack was defined to mean.  It sounds like you are saying you know the angle-of-attack is 11 degrees during takeoff, but you are not sure whether the pitch attitude is 11 - 6 = 5 degrees, or whether the pitch attitude is simply 11 degrees, or something else.
Setting aside the fact that it seems more likely that you would know the pitch attitude and not the angle-of-attack rather than vice versa, the answer to your question is --
In the world of practical piloting, flight-training guides, etc, angle-of-attack is usually defined to mean the angle between the wing's mean chord line and the free-stream airflow or "relative wind", which is equal and opposite to the direction of the flight path.  At the instant of take-off, the flight path is still horizontal.  (Take-off may be defined as the point where the flight path begins to curve upwards into a climb.)  So if the angle-of-attack is 11 degrees at this instant, and the angle-of-incidence (as usually defined in practical aviation, especially in the American context) is 6 degrees, then the pitch attitude of the fuselage would be 11 - 6 = 5 degrees.
When we are talking about a whole aircraft rather than just a part such as just the wing or just the fuselage, then sometimes angle-of-attack is used to mean the angle of the longitudinal axis of the fuselage to the relative wind, in which case at the instant of takeoff in the example above, if the angle-of-attack were stated to be 11 degrees, then the pitch attitude of the fuselage would also be 11 degrees.  But this is not the norm, especially in the world of practical piloting.  Normally angle-of-attack is defined as the angle between the mean chord line of the wing and the relative wind.
When angle-of-attack is defined as the angle between the mean chord line of the wing and the relative wind, a pilot usually does not know his actual angle-of-attack at any given instant, unless he does the math by adding the angle-of-incidence (if known) to the pitch attitude (as visually estimated or as read off the attitude indicator), which is why your question seems a bit odd.  Still, even the exact angle-of-attack may not be known at any given instant, all pilots should understand that it is extremely important to the flight dynamics of an aircraft at any given instant.  Hence it is entirely logical and normal to talk of "increasing the angle-of-attack to maintain altitude in a turn", etc.
To a first approximation, for any given trim setting, the fore-and-aft position of the control stick or yoke serves to control angle-of-attack rather than pitch attitude.  The resulting pitch attitude will be strongly dependent upon climb or descent angle, which is strongly dependent on power setting.  In a sense the fore-and-aft position of the control stick or yoke actually serves as an "angle-of-attack gauge", though this effect is distorted by many different factors such as the curvature of the relative wind in turning flight, propwash effects, "bending" of the airflow over the tail by deflected flaps, etc.  Still, the basic connection between the fore-and-aft position of the control yoke or stick and the angle-of-attack of the wing is one of the reasons for the frequent references to angle-of-attack by pilots, pilot training manuals, etc.
If you are talking to people who aren't Americans, you should know that there is a British usage of the phrase "angle of incidence" that means the same thing as "angle of attack", rather than meaning the angle between the mean chord line of the wing and the longitudinal axis of the fuselage.  You'd more likely encounter this usage in an aerodynamics textbook or a design textbook than in a study guide for a private pilot ground school or written test.
Many other definitions of angle-of-attack exist.  For example one might measure between the mean chord line of the wing and the local airflow, including the effect of the upwash coming into the wing, and any propwash that is may be present.  One can speak of the angle-of-attack of the vertical fin, or the horizontal tail, in which case again one might be measuring relative to the local airflow rather than the free-stream airflow.  Even if one is not considering the deflection of the local airflow by the physical presence of the aircraft, one may, or may not, be taking into account that even the undisturbed free-stream airflow or relative wind is "curved" in turning flight to follow the curvature of the flight path.  In other words the rotation of the aircraft about its axes creates an additional velocity component in the undisturbed free-stream airflow which differs at different points along the length of the aircraft, and effectively makes the relative wind "bend" to follow the curving flight path.  So, it's complicated.  But taking the simple case of linear flight, a good starting point for practical piloting is to take the "angle-of-attack" as meaning the angle between the flight path and the mean chord line of the wing.
Useful related external links--
https://www.av8n.com/how/htm/aoa.html#sec-def-aoa
https://www.av8n.com/how/htm/aoa.html#sec-raoa-aaoa
https://www.av8n.com/how/htm/aoa.html#sec-incidence
Some related ASE questions and answers--
(Q) What is the difference between Angle of Incidence (AoI) and Angle of Attack (AoA)?
(A) What is the difference between Angle of Incidence (AoI) and Angle of Attack (AoA)?
(Q) How common is it in current British usage for the angle between the chord line of a wing and the flight path to be called the "angle of incidence"?
(A) How common is it in current British usage for the angle between the chord line of a wing and the flight path to be called the "angle of incidence"?
(Q) Is there a standard word or phrase in the English-speaking world to describe the angle between the fuselage and the flight path / relative wind?
(A) Is there a standard word or phrase in the English-speaking world to describe the angle between the fuselage and the flight path / relative wind? -- (possibly a non-standard view on the matter)

It seems that using the wing angle-of-attack is more common in small aircraft, which tend to have straight untwisted wings with obvious chord line and not much of a floor to define the body axis, while using fuselage angle-of-attack is more common in large aircraft with twisted swept wings where the chord line varies along span, but they have a lot of floor that clearly defines the fuselage axis (e.g. for A320 the alpha-limit is given as 17° and critical AoA around 20°, which are unrealistic values for any airfoil, so they are clearly referenced to fuselage).

@JanHudec -- interesting, thanks, worthy of an answer

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Why can't you have sail-powered airplanes?
So, sailing boats take the kinetic energy of a crosswind and turn it into thrust by using their sails as lifting surfaces, and the discussion I had in the comment section of this question made me wonder why nobody has ever built any (working) sail-powered airplanes.
Basically, imagine a glider, but with sails on it (maybe on both top and bottom of the aircraft, to avoid imbalances in the center of thrust tipping it over) to catch the crosswind and provide forward thrust. Since these vehicles don't exist, there are presumably problems with them that would prevent them from working.
What are these problems? Do the aerodynamics of the sails interfere with the aerodynamics of the wings or something? Even if sails don't provide enough thrust to get the plane off the ground, that wouldn't be a problem for a glider that can't get off the ground by itself, right?

Won't anyone mention dynamic soaring?

You might as well have a windmill out in the airflow, connected to a generator, connected to a battery, connected to a propeller

@quietflyer: Not quite. Quartering wind can produce sailing speeds in excess of wind speed. But that works only because the sailboat has two media at its disposal and can extract energy from the difference in their respective speeds.

It's disappointing to see downvotes without mention of why the voters feel this question isn't valuable. This is a fair and interesting aerodynamics question, which is non-obvious to those who don't understand how sailboats use their keel and rudder to create lift in the direction of travel. Indeed, most of the answers so far to this question betray a certain unsophistication about the hydrodynamics involved (although they're spot on about the mandatory intersection of two reference frames).

We do have sail-powered aircraft.  They're called kites :-)

Why the multiple upvotes to comment starting "Not quite"?   I still say you might as well have a windmill out in the airflow, connected to a generator, connected to a battery, connected to a propeller.  No relationship whatsoever to the fact that a sailboat, operating on the interface between water and air, can sail at speeds in excess of wind speed at some wind angles.

Re "It's disappointing to see downvotes without mention of..."  -- even if one has no idea how sailboats work, a rudimentary understanding of the fact that an aircraft flies within the surrounding airmass should be sufficient to make it clear why sails would not be beneficial on an aircraft.

Downvoted because once an aircraft is airborne, there is no wind. Wind is nothing more than an air mass which is moving relative to the ground. There is no such thing as wind if you remove the ground as a factor. Imagine a hot air balloon floating along in an air mass. You can hang on it all manner of sails, but it isn't going anywhere, other than where the air mass takes it.

@Kenn Sebesta, my personal rule is to never downvote without offering constructive criticism. In this case, however, I cannot think of a single thing that could improve the question itself. I downvoted because simply asking offends my common sense and disregards basic observations of how the world around us works.

@MikeSowsun which brings to mind a certain reoccuring subject of turning into wind at low airspeed

Thanks to Mike and Michael for explaining their downvotes. For some reason, this conversation jostled my memory of https://meta.stackoverflow.com/a/376313/4271922. It's not exactly a perfect fit, but I believe it's relevant to understanding why some people have what look like easy questions but are in fact not. If the OP were an expert in chemistry/public policy/music/etc..., is it fair to expect a firm grasp of both aeronautical and nautical domains as well? I think from the back and forth on the up/downvotes shows there's a lot of disagreement on this point.

@Kenn Sebesta, you make some valid points, and I appreciate you sticking up for the OP.  My point was less about someone from an outside discipline not having a grasp of advanced aeronautical concepts, and more about what I perceive as a lack of basic understanding about how things work from personal observation.  A child blowing bubbles in the back yard very soon learns that the bubbles drift with the wind. I don't mean this as an insult, but I just cannot fathom how anyone might think that while drifting with the wind it would be possible to deploy a sail and go even faster than the wind.

@MichaelHall For the record, this question was written after considering the forces acting upon a motionless glider in moving air, and not the forces acting on a moving glider in still air, even if they'd be the same thing from different reference points. I hadn't considered the idea that it'd just be blown along with the wind at all.

@nick012000 -- you have to ask the question, "why is the glider motionless?"   Because it just happens to be flying at the same speed that the wind is blowing?  Or because some sort of a tether is exerting a force on it that keeps it fixed in place?  The physics are considerably different in each case.  In the latter case the glider may be able to maintain altitude even if the air has no upward velocity.  In the former case that will never be possible.

@quietflyer Because from its perspective,  its not moving, and everything else is moving around it?

High performance sailboats can sail faster than wind speed in certain conditions. Therefore, your question is not as absurd as it might seem at first glance.
However, the technique that enables sailboats to do so is not available to airplanes, at least not in flight. Sailboats use the speed difference between water and wind. Their keel keeps them from being blown with the wind. A glider in the air has no such second medium to resist being blown away by the wind.
Historically, the Andrée ballon used for artic exploration in 1897 tried to "sail" by combining sails and trailing ropes. However, this did not work in practice.
The only way to extract energy from the wind is when this wind changes. Wind gradients allow albatrosses to soar dynamically, and changing updrafts can be exploited by changing the load factor.

Short version of (by now) two other answers: a sailing vessel needs a sail in one medium and a keel in another: a foil in the water, conventionally; ropes dragging on the ground; electromagnets in the storm wall of Jupiter's Great Red Spot, in a science fiction story; reaction wheels in inertia, in a solar sail.
Slightly longer:  it needs two things (airfoil, "waterfoil", etc.) that exert different forces or at least torques.  When a force is due to fluid (gas or liquid) moving past a foil, lift (in whatever direction is transverse to the foil) is more efficient than drag.

FWIW, it would be more accurate to say it needs a "wing" in one medium and a "wing" in another. A sail is a wing, and some of the more interesting cutting edge sailboats have symmetric wings. Furthermore, the daggerboard/centerboard/keel is a wing as well, and it works specifically because of it's AoA through the water.

Actually, it needs wings in different velocity streams -- don't have to be the same medium.   A submarine could sail against the Gulf Stream, for instance, by floating at the bottom of the flow and extending a keel down into the "still" water below.  Same medium, different velocities.

Excellent point!

Oops, I pocket voted this down (yes, it is possible) and can't reverse that unless this answer is edited...

@Jpe61 here you go!  (btw what's a pocket vote?  google fails me.)

Was checkin out this question, got into a discussion with a colleague and slipped the phone into my pocket without locking the screen. You paid the price

For a glider to move forward using vertical sails, you would have to fix it to the ground somehow, as if it was on tracks, to provide the lateral resistance that allows the reaction force between lateral air movement and the vertical sail to occur.  Something like a kite surfer.  Replace the kite with a regular glider, with a tether line running from the glider's center of gravity to the surface of a lake, and a floating element with the required keel to resist lateral movement at the bottom of the tether line, and there you go.  You have a glider that can move along powered solely by lateral winds, as long as it's anchored to the surface. Until you run out of lake...
Gliders do sail like sailboats, just in the vertical plane.  The wing is doing double duty as the supporting element and the "sail".  A sailboat's sail makes forward thrust from air moving laterally across its path.  A glider's wing, in level flight, needs additional energy from air moving vertically across its path to allow it to move forward without descending, or to climb.  Gravity is the energy source up to the point of the glider's flattest still-air glide angle; additional energy to maintain level flight, or to climb, comes from vertical air motion.
The sailboat needs lateral winds.  The glider needs "vertical winds". I've always called soaring "vertical sailing" and gliders are called "sailplanes" after all.

In a sense, you're right. There is a reason why gliders are also called sailplanes.

A wingsail makes a sailboat into a bit more of a cross between a plane and a boat.

Related-- https://aviation.stackexchange.com/questions/76894/when-do-the-lift-and-drag-vectors-contribute-a-force-component-along-a-gliders/76903#76903 -- when can the lift vector be viewed as having a "forward" component relative to the glider's flight path as viewed from the ground?  Only when when the glider's achieved glide ratio relative to the ground is better than the L/D ratio.  Strictly speaking, this does not require vertical wind.  It can also happen when there is a tailwind, and no vertical wind.

Note that I said "move forward without descending".  My point was that to move forward without descending, or to climb, requires a vertical wind supplementing gravity.

Sail-powered vehicles cannot be faster than the wind they travel in (along the wind direction) and need another medium (ground or water) that offers resistance.
An airplane, to be in flight, needs to move forward w.r.t. the air sorrounding it and cannot be in contact with another medium.
The two are mutually exclusive.
A similar question got a similar answer.

Sail-powered iceboats can travel three times faster than the ambient wind.

@CamilleGoudeseune in the direction of the wind?

Yes, they can go downwind faster than the wind

@DeltaLima darn, now I want to know how the hell that thing works :D

The wheels drive the propeller, 2) the propeller forces the thing to move forward with respect to the surrounding air, 3) The whole thing ends up moving faster than the wind.

Re "@DeltaLima darn, now I want to know how the hell that thing works :D "-- I have one of those things attached to my hang glider

Just kidding ha ha ha

PS that thing is not  "sail powered iceboat", and anything powered by a simple sail cannot travel in a straight line in the straight-downwind direction any faster than the wind is blowing.

This covers a lot of the explanation quite nicely:
https://www.kqed.org/science/8503/how-do-these-boats-sail-faster-than-the-wind#:~:text=If%20a%20boat%20sails%20absolutely,as%20the%20wind%E2%80%94no%20faster.&text=In%20fact%2C%20the%20physics%20that,travel%20faster%20than%20the%20wind.

For the steady-state, uniform condition-- i.e. no changes in wind speed either over time or over space-- we can consider a glider flying within a moving airmass viewed from a reference frame fixed to the ground, as exactly equivalent to a glider flying within a stationary airmass (relative to the ground) viewed from a moving reference frame.  There's no way to distinguish the physics at play between the two cases.
In other words, in an airmass that is uniform over time and space, if you can't actually see the ground, there is no way to tell which way the wind is blowing.  There is no maneuver you can do where the aircraft will respond differently when flying upwind versus downwind versus crosswind.
If you are on the ground looking at a glider flying in a still airmass, it will be obvious to you that putting sails on the glider won't accomplish anything.  If the glider continues to fly in the same airmass but you are now riding in a airplane passing by and viewing the glider from that perspective, would you think that putting sails on the glider would now accomplish something?  Clearly not.
Expecting sails to work on a glider in the presence of a steady, uniform wind, is like expecting sails to work as you watch the glider from the moving airplane as it flies in still air.
Any theory that predicts that the forces acting on an aircraft are different when it is flying upwind versus downwind versus crosswind-- regardless of whether the aircraft has special "sails" or not-- is selecting the ground as a privileged reference frame.  This violates the principle of Galilean invariance.
A sailboat is completely different than a sailplane (glider).  A glider flies inside of the airmass.  A steady, uniform motion of the airmass cannot exert any force on the glider.  (This is true of vertical motions of the airmass, as well as horizontal motions of the airmass.)  A sailboat exists on the boundary between two different fluids-- the water and the air-- so motion of one fluid relative to the other can and does exert a force on the sailboat.
There has been an attempt to "sail" an unpowered balloon in a direction different from the direction of the wind, but this attempt involved ropes dragging on the ground, so that the balloon could no longer be viewed as being "at rest" within the airmass. An equivalent would be a glider rising on a fixed length of cable that is tethered to the ground at one end, which is certainly possible on a windy day.
And then we have Dynamic soaring, which is a completely different "ball of wax", exploiting shear lines, wind gradients, the boundaries of thermal updrafts and downdrafts1, and other spatial or temporal variations in the airmass.
Footnotes:

Links relating to extracting energy from the boundaries between downdrafts and still air via "dynamic soaring" techniques:

https://journals.sfu.ca/ts/index.php/ts/article/view/296
https://www.semanticscholar.org/paper/CALCULATIONS-ON-SOARING-SINK-Kiceniuk/94e63d06de60110c05916a5c4fed1a2197dd8245
https://journals.sfu.ca/ts/index.php/ts/article/view/298

There are some great answers already here, and I normally frown on “me-too” answers, but since I have been critical of the question I wanted to offer a very simple and practical comparison that might facilitate that “aha” kind of clarity in case it hasn’t happened yet...
Picture two things in your mind:

The first is an old fashioned water wheel attached to a mill built
alongside a river.
The second is an old fashioned, stern-wheeled,
Mississippi river boat.

In the first, the waterwheel is passive.  It extracts kinetic energy from the river to do work.  It harnesses the power of the moving water to turn a grindstone.  (or electric generator, or belt that drives machinery...)
The stern wheel of the riverboat, however, is active.  Functionally it might appear similar, but it requires an engine, a power source, outside energy applied to it in order to make it turn and thereby perform work.  Without energy applied to the wheel it simply drifts along in the river just as the boat does.  If the engine quits the boat is dead in the water.
Asking why adding a passive sail to an airplane wouldn’t propel it forward is like asking why you couldn’t just put a prop or wheel in the water and expect it to go.  No advanced engineering or aerospace explanation is needed to understand why this wouldn’t work!
And again, per my comments I don’t intend this as an insult at all.  The question is reasonable, and I have blanked on seeing obvious things before, until something shifted my perspective and the obvious answer came into focus.  Sometimes all that is needed is a different point of view.
I hope this helps.

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text:
How can I compute the minimum possible bank angle for a turn with a given radius?
I know that I can find an upper bound for the bank angle for a plane, if I know the maximum sustained load factor of that plane because the roll angle and the load factor $n_z$ in a turn are directly related:
$$tan (\varphi) = \sqrt{n_z^2 - 1} \;\; \text{or} \;\; \varphi = arctan\left(\sqrt{n_z^2 - 1}\right)$$
And also I known that the bank angle would not be more than 30° for civilian and 75° and more for military aircraft.
But my question is :
How can one get the minimum possible bank angle an airplane can use to perform a turn with a given radius before reaching the stall speed?
Also I want to know if the stall speed is known, can we use the formula :
$$ W = V/R $$
to calculate the angular rate of turn (of course considering the level turn)?

Do these posts contain the answer to your question? https://aviation.stackexchange.com/q/38390/1467
https://aviation.stackexchange.com/q/53875/1467 (that is also by you)
https://aviation.stackexchange.com/q/2871/1467
https://aviation.stackexchange.com/q/26467/1467

And also I known that the bank angle would not be more than 30° for civilian and 75° and more for military aircraft. -- where are you getting 30 degrees?  That's some pretty boring flying you seem to be envisioning--

Given a radius $R$ and a velocity $V$, the bank angle can be computed by:
$\phi = \textrm{atan}\left(\frac{V^2}{R\cdot g }\right)$,
where $g$ is the acceleration by gravity. This shows that the lower the speed becomes, the lower the bank angle becomes. The lowest attainable speed is the stall speed, however we have to take into account the load factor during the turn.
The load factor $n$ during the turn is:
$n=\frac{1}{\cos \phi}$
Due to the increased load factor, the stall speed increases in the turn:
$V_{stall,turn} = V_{stall} \cdot \sqrt n $
The minimum bank angle for a turn with radius R will occur when the speed is equal to the stall speed for that angle.
Solving this mathematically for $\phi$ results in:
$\phi_{min} = \textrm{atan}\left(\frac{V_{stall}^2}{\sqrt{R^2g^2-V_{stall}^4}}\right)$
Note that is the theoretical approach; in practice you would not fly at the stall speed, especially not during turns.
Units are all in SI, you have to apply conversion factors if you want to use aviation units.

Example:

$V_{stall}$ = 50 m/s (approx. 97 knots)
$R$ = 400 m
$\phi_{min}$ = ~39.6 degrees
$V$ = ~57 m/s (approx. 111 knots)

can i know the usual bank angle of the military and the civilian planes. I mean the usual bank angle and hence the velocity, to do a complete turn, or it is not possible to know that information ?

@Ahmed I don't understand what you mean. There are three related variables in simple turn mechanics: velocity, bank-angle and turn radius. If you know two of them, you can calculate the third. For typical aircraft operations, the bank angle and the velocity are controlled by the pilot, the turn radius is the result. For passenger aircraft a maximum bank angle of 25 or 30 degrees is often used. In other cases the radius of the turn is given (see fix radius turn) and the bank angle is the result.

ok i got it, i want to ask you again about the equation, it seems that we can not put bank angle = 90 degree(in coordinated level turn), am i right?

@Ahmed That is right. If the wings roll 90 degrees, the lift vector is fully horizontal. That means there is no vertical component any more to counteract the gravity force. This means that the aircraft will accelerate downwards, and therefore it is no longer a level turn.

Still you do not have a given v, or g, dependent on v.  What one could do is have r variable for chosen speeds, plot on graph, and extrapolate to v stall?  In other words, it may not be possible to turn plane in given radius safely (unless you know hammerhead!).

@RobertDiGiovanni I don't understand what you mean  by your first sentence. g is the acceleration by gravity, approx. 9.81 m/s^2. V follows from the formulas

Plot radius (could be calculated) of safely flown 60 degree bank (knots above stall margain), then same for 45, 30 etc.  Should generate a radius plot comparison. Info from POH accelerated stall speed chart.

DeltaLima is that the g in your turn?  Will try my (slightly old fashioned)plot  for Cessna 172 POH data.

@RobertDiGiovanni no, the "g in your turn" is the load factor, "n". For 60 degrees, n = 2, which means it is a 2g turn.

So, please could you show a radius of a 60 degree, 2 G turn at 100 knots?

Found on web R feet = V squared knots/(11.26 × tan bank angle).  Any thoughts?

Let us continue this discussion in chat.

TL;DR: just assume that you are flying at your stall speed and compute the bank angle from there.
Please do not fly at your stall speed, especially not in a turn, you will stall and could have serious problems
Assuming you are flying at your stall speed $V_{stall}$, and you want to have a turn with radius $R$, you will need to have a turn rate of
$$\dot\psi = \frac{V_{stall}}{R}$$
and a bank angle of
$$\phi = atan \left( \frac{V_{stall}^2}{g \cdot R} \right) $$
(where $g$ is the gravity acceleration) will let you fly in a coordinated way.
All terms are in SI units.

@Ahmed you cannot fly below stall speed, so that's the angle. yes, each aircraft will have a different stall speed, and thus a different "minimum angle", but the answer does not change.

Stall speed depends on load factor, so in a coordinated level turn the stall speed will be higher than in straight and level flight. That should be factored in...

@CptReynolds indeed. See my answer.

@DeltaLima Perfect!

Since we know the radius, could one work it as a half circle, with the circumference as 1/2(2piR) = piR.  For a given speed, delta v in the half circle would be 2x entry speed v.  The transit time would be distance/v. G would be delta v/t.  That's as far as I got.  Minimum safe radius would be excellent POH info for any aircraft, particularly large.

"you could have serious problems": well, that a nice understatement! Or a different way to say that you could die.

How can I compute the minimum possible bank angle for a turn with a
given radius?

No computation is needed; the answer is zero degrees.  Apply rudder as needed to turn, while cross-controlling with the ailerons as needed to keep the bank angle at zero.
(Note: if you are trying to achieve an extremely low turn radius in relation to your airspeed, you might "run out of rudder" before achieving your goal.  To say whether or not this will happen, requires more information than is contained in the question.  If you are thinking in the ballpark of the kind of turn radius that could be accomplished with thirty degrees of bank or less, as your question seems to indicate, this will probably not be an issue.)
(Did you intend to specify that the turn should be "coordinated", i.e. non-skidding?)

I know that I can find an upper bound for the bank angle for a plane,
...
And also I known that the bank angle would not be more than 30° for
civilian and 75° and more for military aircraft.

The last quoted sentence above is unfounded.  There's no basis for those limits.


text:
What is the difference between a glider and a sailplane?
The words "glider" and "sailplane" seem to refer to similar or the same type of aircraft. In particular, the Wikipedia articles "Glider (aircraft)" and "Glider (sailplane)" seem to be describing the same kind of aircraft.
What is difference between a glider and a sailplane, if any?

Interestingly in Australia (in my experience) we just call 'em gliders (sailplane sounds like an American term to me). glidingaustralia.org never mentions sailplanes at all.

The sailplane article is focused around sport and recreational planes. The aircraft article describes a wide variety of aircraft, not simply planes, like hang gliding and paragliding.
Which makes sense - one is about aircraft, so it has the aircraft moniker. The other is specifically about planes, which are a subset of aircraft, and thus have the sailplane moniker.
There was an idea of merging them in 2011, but it failed.

Any airplane can be a glider.

@mins both sentences are true. They are not mutually exclusive. According to the referenced wikipedia article "Glider is the agent noun form of the verb to glide." So any airplane that glides is a glider by definition. ;)

@Devil07: Any aerodynamically stable airplane. That used to be a prerequisite for any airplane to be controllable in flight so the phrase "any airplane can be a glider" was true. These days we have weird computer stabilised aircraft that won't glide without engine thrust.

From the FAA Glider Flying Handbook, pages 1-3 and 1-4:

The Federal Aviation Administration (FAA) defines a glider
  as a heavier-than-air aircraft that is supported in flight by the
  dynamic reaction of the air against its lifting surfaces, and
  whose free flight does not depend principally on an engine. ...
Another widely accepted term in the industry is sailplane. A
  sailplane is a glider (...) designed to fly efficiently and gain
  altitude solely from natural forces, such as thermals and
  ridge waves. Older gliders and those used by the military were
  not generally designed to gain altitude in lifting conditions.

(Emphasis mine)

There does not appear to be any formal definition I can find, but if one observes the aircraft that are typically described as a 'glider' or a 'sailplane'...
Sailplane is generally used to describe an unpowered aircraft that is optimized to remain airborne by taking advantage of thermal currents. Typically lightweight, typically with very long wings. Schweitzer is a well known maker of sport sailplanes.
Glider refers to an unpowered aircraft that isn't necessarily optimized to remain airborne in the non-towed state. Aircraft described as 'gliders' are usually WW2 aircraft for getting troops and equipment onto unprepared ground, hopefully in one piece. They were used for airborne assault in pre-helicopter days. Examples: Waco CG4, Airspeed Horsa, DFS-230, ME-321. (the ME323 Gigant was the powered version) All were expressly designed to be towed to their destination by powered aircraft, and make short glides onto unprepared ground, to deliver troops and equipment.
Also, rocket propelled aircraft such as the ME-163 were described as a glider, when their fuel ran out. Not sailplane.
Finally, quite a few aircraft under development in the pre-CAD era were first flown as unpowered versions. Those experimental aircraft are always referred to as 'gliders'.

"Glider" is the broader term, including everything that would normally be described as a "sailplane", and also including many other aircraft such as troop-carrying assault gliders, and ultra-low-performance training gliders like "primary" trainers and training gliders adapted from light airplanes such as the Piper TG-8, and rocket-powered gliders such as the ME-163 Komet, and even the Space Shuttle.
"Sailplane" generally confers a connotation that a given aircraft is intended to actually gain altitude in soaring flight.  Yet there are also some craft called "gliders" that are specifically intended for soaring, yet would never be called "sailplanes".  These include weight-shift controlled hang gliders, and paragliders.  As an aside, being ultralight aircraft, note that these aircraft do not actually fit within the glider "category" as defined by the FAA.
If a given aircraft is not generally shaped like a streamlined, efficient version of a conventional airplane, or is not guided by a pilot using a fairly "conventional" aircraft control system, it will probably not be called a "sailplane", no matter how well it can soar.
There are also some aircraft that most people would agree may fairly be called "sailplanes" as well as "gliders", yet would not fit within the "glider" category as defined by the FAA  because they are ultralight aircraft.  An example would be the Archaeopteryx foot-launchable sailplane.

Also, the Space Shuttle was a glider when returning from orbit, but one would hardly call it a sailplane :-)

@jamesqf - yep - thanks - noted

I have no issue with either answer given.  That said, I think this question deserves an answer "from the street".
I got my glider add-on in the summer of 2016, started training for it in the summer of 2015.  I belong to a 100+ member glider club in the United States, of which 85 percent have their glider certification/add-on, 20 percent are CFIs and quite a few have flown gliders for 40+ years.  Due to the nature of our club, during my training I flew with 15+ different instructors.  And, of course, given the "stand around and tell war stories" nature of glider operations, I've talked glider flying with most of my fellow club members.  During all flights I have undertaken and observed, the primary goal was ALWAYS to "remain airborne by taking advantage of thermal currents." (though we don't call them "currents").  The exception, of course, is training flights, where the primary objective was learning to fly gliders.
All of this said, I have NEVER, not once, heard the aircraft we fly refered to as a "sailplane".  On the contrary, the word we use to refer to what we fly is glider, exclusively.

Gee, aren't there plenty of references to "sailplanes" in the magazine published by your national organization, the SSA?  And note that this book is called "sailplane aerobatics" https://www.amazon.com/Sailplane-aerobatics-Horvath/dp/B0006EK6XQ

Unfortunately, @bclarkreston, 2017 version no longer exists...so no answer will be forthcoming.

The term "glider" has many usages. It can mean any unpowered object, from lizards to underwater craft, supported by wings and able to convert part of its downward motion into significant forward motion. Most commonly it describes any unpowered fixed-wing aircraft, some of which have quite steep and short flight paths.
The more streamlined gliders can soar, which is a form of gliding in which rising air currents are used to sustain flight more or less indefinitely. Such a soaring glider is commonly called a sailplane.
Then there are the specialist technical definitions, such as that used by the American FAA certification authority.
Many glider clubs exist and most of their planes are of the sailplane class of glider, however they are typically referred to as gliders by their owners and pilots.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What class is the airspace at KGCN when the tower is closed?
I was wondering if someone could help me figure out how the airspace around the Grand Canyon National Park Airport (KGCN) works. The chart supplement here says:

AIRSPACE: CLASS D svc 1 Jun thru 30 Sep 1300–0300Z, 1 Oct thru 31 May 1400–0200Z other times CLASS G.

... but the Grand Canyon VFR chart here says:

See NOTAMs/Directory for Class D/E (sfc) eff hrs

The VFR sectional just shows a class D ring around the airport with a class E surface area extension to the southwest:

When the tower is not occupied, how is the airspace around KGCN arranged?

It may be an error on the chart, it should be either Class D or Class G, but it depends...
If the ATIS reverts to ASOS when the tower is closed, the airspace can be Class E. If ATIS/ASOS is not available, then the airport has to be Class-G. I would stick with the chart supplement here:
June 1 through September 30th, the tower is manned from 1300Z to 0300Z and is Class D. October 1 through May 31 the tower is manned from 1400Z to 0200Z and is Class D. All other times it is Class G meaning they do not have ASOS available. (AWOS is available by phone).
So according to the chart supplement, if the tower is not occupied the airspace is Class G.

One or the other document is out of date I suppose.

What is the error? I don't see anything that doesn't coincide.

@TomMcW The chart graphic says it will be either "D or E", and directs you to the supplement while the chart supplement says that it will be either D or G.

@RonBeyer I read it as saying that both the class D and E sfc areas are inactive after hours. They should both revert to G, at least below 700 feet.

I see where you're coming from now. It's the way they worded it. I don't think they intended to indicate that D reverts to E, but that both areas have effective hours

@TomMcW -- "I don't think they intended to indicate that D reverts to E, but that both areas have effective hours" -- yes, that's exactly it.  Explained better here https://aviation.stackexchange.com/a/92302/34686 than in my answer to the present question.

2022 Update: The "Long answer" portion of the answer has been updated to reflect some recent corrections on the sectional charts.  Rather than re-write the answer to reflect a situation different from what existed when the question was asked, the updates have been in the form of superscripts that key to footnotes.  A more concise explanation of the current (corrected) situation in regard to the tags on the sectional charts themselves may be found in  this related ASE answer, beginning with the paragraph that starts "You should be able to tell the same information from the sectional chart itself."

Short answer
The chart supplement told you what you needed to know.

AIRSPACE: CLASS D svc 1 Jun thru 30 Sep 1300–0300Z, 1 Oct thru 31 May
1400–0200Z other times CLASS G.

means that the Class D becomes Class G airspace when the tower is closed.  It never happens that Class-E-to-surface "extensions" remain in effect when the adjoined airspace reverts to Class G, so they revert to Class G as well.
You could not have known this for certain just by looking at the sectional chart.1  Read on to learn why.

Long answer
"See NOTAMs/Directory for Class D/E (sfc) eff hrs" is the standard chart notation used in a case where the Class D airspace, and its associated Class E-to-surface "extension", both revert to Class G airspace when the tower is closed.
For example, we can find an identical notation on the chart at KARD at Ardmore, OK.
It never happens that a Class-E-to-surface "extension" remains in effect when a Class D airspace reverts to Class G airspace.
However, if the Class D airspace reverts to Class-E-to-surface airspace, then the airspace in the Class-E-to-surface "extensions" invariably remains Class-E-to-surface airspace.  In this case, the chart notation often but not always2 simply reads "See NOTAMs/Directory for Class D eff hrs".  See for example KMFR at Medford, OR.  Unfortunately, in some instances, the tag "See NOTAMs/Directory for Class D/E (sfc) eff hrs" is used in this situation as well3-- hence the need to check the Chart Supplement whenever this label appears.  More on this below.
Another way to definitively find out what the situation is at KGCN, is to check the FAA's "Airspace Designations and Reporting Points" document, current edition (August 2019) Order JO 7400.11D.
The Class D airspace at Grand Canyon National Park airport is listed on page D-138, including the notice "This Class D airspace area is effective during the specific dates and times established in advance by a Notice to Airmen. The effective date and time will thereafter be continuously published in the Airport/Facility Directory."
If the Class D airspace reverted to Class-E-to-Surface rather than Class G when the tower closed, we would find a duplicate listing in the "E2" airspace section of the "Airspace Designations and Reporting Points" document.  It would be on page E-128, between the listings for Douglass and Prescott.  No such listing appears. Therefore the Class D airspace reverts to Class G airspace when the tower is closed.
It never is the case that a Class-E-to-Surface "extension" remains in effect when the adjoined airspace reverts to Class G.  When the Class D airspace reverts to Class G, so does the Class-E-to-Surface "extension".  We can confirm this by checking "E4" airspace section of the "Airspace Designations and Reporting Points" document.  The listing appears on page E-205, and contains the note "This Class E airspace area is effective during the specific dates and times established in advance by a Notice to Airmen. The effective date and time will thereafter be continuously published in the Airport/Facility Directory."
The August 3, 2017 version of the document, JO 7400.11B, which was in effect when the question was originally asked, gives the same answers.  The relevant page numbers are D-139, E-129, and E-213.
A word of caution-- one would think that chart notation "See NOTAMs/Directory for Class D/E (sfc) eff hrs" would be a reliable indication that the Class D (and therefore the attached Class-E-to-surface extension) all revert to Class G airspace when the tower is closed.  If the airspace all becomes Class-E-to-surface airspace when the tower is closed, so none of the surface-level Class E airspace vanishes, shouldn't the chart notation always simply say "See NOTAMs/Directory for Class D eff hrs"-- as it does in the example at given above at KMFR at Medford, OR?
In fact, the tag "See NOTAMs/Directory for Class D/E (sfc) eff hrs" is not a reliable indication that the Class D airspace, and the associated Class-E-to-surface extension, revert to Class G when the tower closes.4  It is sometimes also used in cases where the Class D airspace reverts to Class-E-to-surface airspace, and the airspace in the "extensions" also remains Class-E-to-surface airspace.5  This is an unfortunate artifact of some FAA arcanery.
In more detail-- the FAA actually has two different ways of handling the situation where a Class D airspace, with Class-E-to-surface "extensions", reverts to all Class-E-to-surface airspace when the tower closes.
The more common way is for the E4 Class-E-to-surface "extensions" to be in effect 24/7 and for the Class D airspace to revert to E2 Class-E-to-surface airspace.  This is when we always see the tag "See NOTAMs/Directory for Class D eff hrs", as at KMFR at Medford OR.
The less common way is for the E4 Class-E-to-surface "extensions" to close along with the Class D airspace, and for the "extensions" along with the Class D airspace to be replaced with a single E2 Class-E-to-surface airspace with the identical footprint.  In this case the cartographic staff has apparently sometimes been confused by the tag in the "Airspace Designations and Reporting Points" document indicating that the E4 airspace is not in effect 24/7, failing to notice that it is fully replaced by E2 airspace which is still surface-level Class E airspace.  As a result, in this case we see sometimes see the tag "See NOTAMs/Directory for Class D/E (sfc) eff hrs"6 instead of the tag "See NOTAMs/Directory for Class D eff hrs".  An example of this is KPRC at Prescott, AZ.7
This related ASE answer gives a list of 21 airports that the FAA has handled in this manner.  Of these 21, 11 (KGCK, KJEF, KNHK, KCXY, KUNV, KNTU, KMKG, KRST, KGFK, KILN, and KPRC) have the sectional chart notation "See NOTAMs/Directory for Class D/E (sfc) eff hrs"8, while the remaining 10 have the sectional chart notation "See NOTAMs/Directory for Class D eff hrs".  There appears to be no particular reason for the variation.
Footnotes:
1,2,3,4,5,6,8:  Update 2022: this situation has apparently now been fixed (except for two remaining "holdouts" which are KNHK and KNTU) and therefore it appears that in the particular case of airports where the Class D airspace has one or more surface-level Class E extensions, the occurrence of the phrase "See NOTAMs/Supplement for Class D/E (sfc) eff hrs" on the sectional chart therefore now can be taken as a reliable indication that when the tower closes, the surface-level controlled airspace reverts to Class G airspace. After this correction, the phrase "See NOTAMs/Supplement for Class D/E (sfc) eff hrs" is no longer used in any cases (again except for KNHK and KNTU) where when the tower closes, the airspace in the "extensions" remains surface-level Class E airspace (and the Class D airspace becomes surface-level Class E airspace)-- even in cases where the oddities of the "Airspace Descriptions and Reporting Points" document are such that the airspace in the "extensions" is designated to switch from E4 surface-level Class E airspace to E2 surface-level Class E airspace when the tower closes.  For more, see this related ASE answer.  It still remains the case that if the Class D airspace has no adjoining surface-level Class E "extensions", then the phrase "See NOTAMs/Supplement for Class D eff hrs" will always be used on the label on the sectional chart, regardless of whether the Class D airspace reverts to surface-level Class E airspace, or to Class G airspace, so in this case the Chart Supplement must be consulted to determine which is the case.
7: KPRC in Prescott AZ, KMKG in Muskegon MI, and KILN in Wilmington OH are no longer good examples of this case, because their surface-level Class E "extensions" have been entirely removed.

Re "Update 2022: this situation has apparently now been fixed"-- actually, KNHK and KNTU still have the faulty notation on the sectional chart, reading "See NOTAMs/Supplement for Class D/E (sfc) eff hrs", even though their airspace is actually in effect 24/7. Latest chart checked: Washington sectional chart effective beginning March 24 2022.  But I now understand that this is scheduled to be corrected in the sectional chart effective beginning May 19 2022.  (Would've skipped last edit if had been aware of that already at the time!)

Re the "short answer"-- "Class D becomes Class G airspace"-- perhaps should clarify that this is at the surface-- Class E airspace begins 1200' above--


text:
What does "MOA excluded" when Restricted Airspace active mean?
Looking at the VFR chart at 453507N1194903W there is a note:

"BOARDMAN & BOARDMAN LOW MOAS EXCLUDED WHEN R-5701 & R-5706 ARE ACTIVE"
What is being excluded here? The military's use of the MOA (so the MOA is "cold" and safe for the general public to use) or the general public's ability to use the MOA (so the MOA is hot, and while possibly legal for the public to use, definitely not recommended or maybe even prohibited)? What does this message mean?

First, to answer your specific question:

What is being excluded here? The military's use of the MOA (so the MOA
is "cold" and safe for the general public to use) or the general
public's ability to use the MOA (so the MOA is hot, and while possibly
legal for the public to use, definitely not recommended or maybe even
prohibited)?

Actually, the chart makers are not intending that this particular phrase should be understood to convey any information about whether, when the Restricted Areas are active, the MOAs will or will not also be active. The label is just attempting to let you know that whenever the Restricted Areas are active, any airspace that they share with the MOAs temporarily "drops out" of those MOAs.
I've now received confirmation that this understanding is correct, in a response to an inquiry I submitted to the FAA's on-line portal for Aeronautical Inquiries.  The response included the sentence "I recognize that the exclusionary verbiage could be confusing".
Some MOAs are set up this way, and others aren't.  MOA boundaries are given in "FAA ORDER
JO 7400.10E", entitled "Special Use Airspace".  The Boardman MOAs are described on pp. 172-173.
Other examples of places where this same pattern of verbiage appears on the VFR sectional charts includes the San Diego sectional chart between Yuma Az and the Salton Sea, and the area NE of Fallon NV on the Reno sectional chart.  But the "Eglin E" MOA near Destin FL does not include a similar label, and the description of this MOA in JO 7400.10E doesn't say anything about carve-outs for the Restricted Areas when they are active.
Arguably a clearer chart label would read something to the effect of "WHEN ACTIVE, R-5701 and R-5706 ARE EXCLUDED FROM BOARDMAN & BOARDMAN LOW MOAs."  The current label seems to get it backwards-- near Boardman, when the Restricted Areas are active their airspace is carved out of (i.e. "excluded from") the MOAs, not the other way around.
In fact, since the information seems to have no operational relevance anyway, it might better be placed on the table of MOA descriptions that appears in the left-hand margin of every sectional chart, than on the actual map portion of the chart.  A single line of text at the bottom could be keyed to all the appropriate MOAs in the table.
I would suggest that the current language risks giving the pilots the impression that the airspace1 in the Boardman and Boardman Low MOAs may sometimes be excluded from the Restricted Areas R-5701 & R-5706. This would seem to go against the interests of safety, and to increase the risks of inadvertent violations of the regulations.
Footnotes:

Arguably the current label can't be unequivocally judged to be "wrong" if one takes the attitude that what is being "excluded" from the Restricted Areas (when they are active) is the characteristic of also being a MOA, not the airspace of the MOAs.  But this is a convoluted way of thinking, and doesn't mirror the language of JO 7400.10E.  Still, the issue is logically "squirrelly" enough that it might be hard to convince the FAA's Charting Group that a change to the established practice is really justified.

Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed.


text:
How does an aircraft's weight affect the V-n diagram?
I have a reasonable understanding of what a V-n diagram shows and what the envelope and the boundaries mean. However, the question I have is how does the weight of the aircraft specifically affect the diagram?
I know that reducing the weight will mean a lower load factor and therefore potentially more manoeuvrability. But is there a mathematical way of showing this? Also, how does the weight relate to lift? Again, lower weight means less lift is needed. But how does that specifically affect the V-n diagram?

Highly related -- https://aviation.stackexchange.com/a/13140/34686

I recommend "Aerodynamics for naval aviators" which is now available as a free PDF. (As I recall it is hosted on the FAA website.) It covers this issue and with better reliability then any answer you will get here. Generally aircraft are complex structures and each sub component has its own limits, and then you must define "maneuverability" as it pertains to engineering or to operation, using strength or aerodynamic limits. This is all further complicated by some rampant misinterpretations of an FAA reg regarding Va and required *design load factor for the old arbitrary normal/utility cat..

When an aircraft is heavier (say wing tanks or fuselage tanks full of fuel), a given amount of pounds of force generated by the wings results in a lower G-load and thus less force on components of fixed weight, like the battery or engine(s).  Therefore the mounts holding these parts of the aircraft in place are subjected to less stress.  Therefore the maximum amount of force the wing can be permitted to exert --measured in pounds or Newtons, not G's-- can be raised-- again assuming it's the stress on things like the motor mounts, etc that we're concerned about-- and that's why the maneuvering speed (Va) in many aircraft  increases as aircraft weight is increased.  (Below maneuvering speed, the wing will stall before generating some critical amount of force that has been judged by the designer to be too much.)
A simpler way to state this is that if we are setting the maneuvering speed to protect the mountings of items of fixed weight, then all that matters is the max G-load that we allow the aircraft to develop.  When the aircraft is heavier, for any given G-load, the stall speed will occur at a higher airspeed.  Maneuvering speed is the speed where the aircraft will stall before exerting so much force that it damages the structure.  So if we are setting the maneuvering speed to protect the mountings of items of fixed weight by not allowing the aircraft to exceed some given G-load, then we can increase the maneuvering speed as we increase the weight of the aircraft.
On the other hand, if were worried about ripping the wings off the fuselage-- if that was the limiting factor in setting our limiting speed-- then it wouldn't make any sense to raise our limiting speed as we increase aircraft weight, at least if all the increased weight was going into the fuselage.  In a simplified case where the weight of the wing is negligible compared to the weight of the fuselage, when the wing is generating X pounds of lift, the same amount of force is being transferred from the wing to the fuselage, regardless of how heavy the fuselage is and therefore what the G-load is.  If the weight of the wing is not negligible compared to the weight of the fuselage, then adding weight to the fuselage means a lower percentage of the wing's lift force will be "absorbed" by the wing itself, and for a given X pounds of lift force generated by the wing, the force exerted by the wing on the fuselage, and the stress on the wing-fuselage connection, will go up as we increase the aircraft weight.  In such a case, if the wing-fuselage connection is our critical concern, then it would make sense for the maneuvering speed to go down as the aircraft weight is increased. On the other hand if the extra weight is going into the wing (fuel, external stores hung from the wings) then for a given X pounds of lift generated by the wing, some of the wing's lift force will be "absorbed" by this weight and the total G-load in any given situation will be less and there will be less force transferred from the wing to the fuselage and less stress on the wing-to-fuselage mounting, so again it would make sense to raise the maneuvering speed as we increase the aircraft weight, if areas such as the wing-to-fuselage mounting are the critical concern.
Similarly, if more of the weight is distributed along the wingspan, the bending stress on the wing spars will be less, for a given total force in pounds generated by the wing.  So if the wing spars are the critical component of concern that governs our choice of maneuvering speed, then if we increase weight by adding it to the wing, the maneuvering speed should go up, but if we increase weight by adding it to the fuselage, the maneuvering speed should go down.
So, it's complicated.  The simplest case is when the limiting concern is the stress on the mountings of items of fixed weight, such as motor mounts, battery brackets, etc, as described at the start of this answer.  My understanding is that that is in fact this most common case and explains why on the Vn diagram, the maneuvering speed typically goes up as the aircraft weight goes up.  Again, in this case we are simply setting a maximum allowable G-loading.
"Maneuvering speed" is not explicitly shown on the figure linked in the question, but generally, it occurs at the point where the line representing the max G-load allowable meets the curved left edge of the envelope representing the stall, with some extra safety margin added.  The discussion above of whether the maneuvering speed Va should be raised or lowered as we add weight to the aircraft, depending on where we are adding the weight, is exactly equivalent to a discussion of whether we should raise or lower the limiting G-load, or neither, as we add weight to the aircraft.  Note that on the V-n diagram, adding weight to the aircraft will shift the curved left edge of the envelope representing the stall further to the right.  You can see how, if our goal is simply to set the maneuvering speed in a way that prevents the aircraft from exceeding some fixed maximum allowable G-loading,  then an increase in weight will automatically change the V-n diagram in a way that increases the maneuvering speed in proportion to the square root of the increase in the weight.  However, if the goal is to limit the stress on the wing spars, or the wing-to-fuselage connection, then the situation may be completely different, depending on where we are adding the weight.
(The diagram linked in the answer doesn't show this, because it doesn't show the stall speed for different weights.  Rather, it shows a change in IAS stall speed with altitude, which is likely related to Mach effects, and not something that we have to concern ourselves with in lower-performance aircraft.)
Related ASE questions and answers--
Q: What is Vg in this VG diagram?
A:  What is Vg in this VG diagram?" -- in this case the aircraft (glider) was assigned a higher Vg, the maximum speed allowed in gusty conditions, as well as a higher Vne, when it was carrying less weight.  The opposite of what we often see in regard to the maneuvering speed, Va, in light airplanes.  So-- as indicated in the present answer-- "it's complicated".

Also highly related -- https://aviation.stackexchange.com/a/42614/34686

(fixed typo after "community" bumped up to top of stack-- not sure why "community" action not showing in edit history)

+1 for the detailed analysis. It's interesting to note that in the F-4J example I given in my answer, putting weight on the wing by e.g. loading wing stores causes a reduced g-limit compared to loading centerline stores, with the same gross weight, as wing bending considerations might be out-weighted by other factors, such as the g-limit of the store itself. But the case can be completely different with heavier aircraft, as wing bending could be more of a problem.

Well, answering your first question, the airplane weight does not really affect the V-n diagram because this diagram is developed knowing the structural forces that the airplane can take without being damaged.
Answering your question about the relation between the maneuverability and the airplane weight, the relation is just a "simple" physics problem. You just need to know the airplane characteristics like the center of gravity, the different aerodynamic factors and the effect of deflecting the control surfaces. When you solve the six equations with six variables of the differential system you can find how any characteristic of the airplane affects its maneuverability.

Finally, as you say, when the weight is low, the needed lift is less but this does not affect the V-n diagram because n stays more or less constant because:
 $n=\frac{L}{W}$. This diagram just shows us which are the relation between the aerodynamic forces and the weight. We all know that the weight is one of the problems for an airplane but it also helps to alleviate the bending moment on the wing root, that is why the last fuel tanks that are emptied on an aircraft are the ones that are further away from the fuselage.

I'll be using the Vn chart for A-10A and F-4J as an example, showing the effect of weight on both subsonic and supersonic planes.
There're two aspects in the V-n chart that takes weight into account:

The lift limit line, at the left boundaries of the chart, representing the stall or flights at critical AOA if such AOA is attainable.
The structural limit, at the upper boundaries of the chart, representing the operational load factor limitations.

V-n ($n_z$) chart of A-10A with 30000 lbs gross weight:

V-n chart of A-10A with 46000 lbs gross weight:

A sea-level V(Mach)-n chart of F-4J with 3 different gross weights:

For the lift limit, the maximum available lift at critical AOA is fixed with the same condition, e.g. the same dynamic pressure (affects total lift with the same $C_L$), elevator position (which can be limited by the pilot or flight control system), static margin (which affects the lift generated by the elevator for pitch trimming, and also the pitching moment characteristics for a change in maximum attainable AOA), altitude, mach number (affects $C_L$), etc. So the fixed maximum available lift at stall, combined with an increased weight, results in a reduction of the achievable load factor, by the equations listed below, and that's why the lift limit line moves to the right as weight is increased.

$n$ = (lift + thrust * sinα) / weight
$n_z$ = normal force / weight = (lift * cosα  + drag * sinα) / weight

It's also interesting to note which load factor the V-n chart is using. For example, the A-10A chart is specific that normal load factor is used, but the F-4J chart only says 'acceleration', so you can only guess. But if you assume AOA=0, then they both equals to Lift / Weight.
For the structural limit, things would get pretty complicated, e.g. if you consider bending moment (like some aircraft such as C-5 and F-22, deploys symmetric upward aileron deflection to reduce wing bending by reducing lift at outer wing sections), mach number (as g-limit decreases at transonic and supersonic speeds), asymmetric maneuvers like rolling (with increased pitching moment caused by inertial roll coupling), and non-steady streams (like gust and dynamic pitching maneuver from the contribution of $C_z$q and $C_z$$a$-dot).
But I'll keep it simple and assuming we're subsonic with steady streams, and weight is added only at center of gravity, wing bending is neglected and the wing is perfectly aligned with the body X axis. So the total force that is perpendicular to the wing is the normal force.

normal force = $n_z$ * weight

Consider an important quote from one of the flight manuals: The aircraft structure, particularly the wings, can only withstand certain maximum forces acting on it.
So the normal force is fixed if neglecting all the above factors, and a decreased weight would mean a higher $n_z$ limit for the structure. But $n_z$ will also cap at a fixed design limit. So what you'll see is basically a decreased g-limit if weight is increased above a certain threshold:

Coincidentally the maneuvering speed doesn't change in these charts, as the lift limit moves to the right and at the same time, the structural limit moves downwards.

Thanks, these are some insightful charts that help illustrate that the physical structural limitations on an aircraft are a function of aerodynamic loads, and therefore the load factor at which structural limits are reached decreases as aircraft weight increases.
However, for planes certified under 14 CFR Part 23 as an example, limits are set in terms of load factor, without allowing for for increased load factors at lighter weights, which would still respect the structural limitations of the aircraft.

Do you have any resources as to why this is the case? It certainly seems simple, and load factor maps more directly to what a pilot feels during operation, but I'd love to find better references that say why this is the case, especially when it is at the expense of restricting aircraft capabilities at weights less than max.


text:
What is the floor of the class E airspace near KRHV when the tower is closed?
See the attached diagram snippet for KRHV in Northern California. The chart supplement says that when the tower is closed the airport surface is class G. At this time, what is the floor of class E in areas "1" and "2"?
As you can see, class E starts at the surface around the Fairgrounds visual reporting point. Class E starts at 700 ft. AGL South-West of the airport and at 1,200 ft. AGL North-East of the airport. What happens in the middle in areas "1" and "2"? Does the magenta vignette cut through class D as shown by the red line or follows the border of class D? Again, this question is only relevant when the tower is closed.

Have you checked the chart supplements for KRHV? It reads "AIRSPACE: CLASS D svc 1500–0600Z‡; other times CLASS G" which might answer your question.

@svoop, he stated this much in the question.  He wants to know where the top of the G, or bottom of the E is.

P.S.  I don't know enough to answer, but I think your presumption about the red line you drew makes sense.  Because D goes away, so too should its border...

Short answer:
When looking at the airspace depiction on the sectional chart, it is logical to assume that the linear portion of the edge of the transition area with 700' floor, shown by the shaded magenta boundary, continues on through the blue segmented circle around KRHV, and this controls the floor of the Class E airspace in that area when the tower is closed and the Class D airspace reverts to Class G.  In that case, the Class E floor in area "1" is 1200' AGL and the Class E floor in area "2" is 700' AGL.  Similarly, it is logical to assume that the arcing circular edge of the 700'-floor transition area located north of KRHV also continues into the blue segmented circle around KRHV, but this section just barely extends into the blue segmented circle before it is intercepted by the linear edge of the 700'-floor transition area coming up from the southeast.
Long answer:
(Click here for a larger view of sectional chart centered on area of interest)
The ultimate authority for the answer to your question is found in the FAA's "Airspace Designations and Reporting Points" document, current edition Order JO 7400.11D.  The class D airspace for KRHV is described on page D-156 under the heading "AWP CA D San Jose Reid-Hillview Airport, CA".  No corresponding E2 airspace is listed-- it would be on page E-134 if it were present.  This confirms what we read in the Chart Supplement-- that the Class D airspace for KRHV reverts to Class G, not Class-E-to-surface, when the tower is closed.  The only exception is the small slice of airspace centered around the "6:30" position of the segmented blue circle around KRHV which does revert to Class-E-to-Surface when the Class D is inactive-- because it is part of an E3 "extension" associated with San Jose International (page E-153).
The magenta shaded border projecting southeast from the word "Evergreen" on the chart is the eastern edge of a "transition area" whose floor is 700' AGL, and your question is essentially asking whether this edge extends on into the segmented blue circle around KRHV, or deviates to include the entire segmented blue circle, or deviates in some other way.  Transition areas are "E5" airspace, and are described starting on page E-220 in the "Airspace Designations and Reporting Points" document.  The specific transition area we are interested in is described on pages E-960 through E-961, under the heading "AWP CA E5 San Jose, CA, San Jose International Airport, CA".  When reading this text, it is helpful to know that "San Martin Airport" (KE16) was formerly known as "South County Airport of Santa Clara County".
Here is the complete text of the E5 airspace description, with the relevant portion highlighted:

That airspace extending upward from 700 feet above the surface within a 5-mile radius of the San Jose International Airport and within 4.3 miles each side of the NAS Moffett Field TACAN 157° radial extending from the NAS Moffett Field TACAN to 20 miles southeast of the TACAN and within 4 miles each side of the 139° bearing from the San Jose NDB, extending from the 5-mile radius of the San Jose International Airport to 24.3 miles southeast of the NDB and within a 6.9-mile radius of the South County Airport of Santa Clara County and that airspace bounded by a line beginning at lat. 37°30'00"N, long. 121°52'04"W; to lat. 37°22'00"N, long. 122°08'04"W; to lat. 37°22'00"N, long.122°24'04"W ; to lat. 37°30'00"N, long. 122°27'04"W, thence to the point of beginning. That airspace extending upward from 1,200 feet above the surface bounded on the north by lat. 37°30'00"N, on the east and northeast by long. 121°50'04"W; and the southwest edge of V-107, on the southeast and south by the northwest edge of V-111, and lat. 37°00'00"N, and on the west by the east edge of V-27 to lat. 37°30'00"N.

The 8-mile-wide strip of 700'-floor E5 airspace that extends 24 miles to the southeast of the San Jose NDB comes all the way up to the 5-mile-radius arc around San Jose International, and does not deviate either to avoid, or to completely include, the airspace enclosed by blue segmented circle around KRHV.  Likewise the curving edge of the 5-mile-radius-circle of 700'-floor E5 airspace around San Jose International continues a short ways into the blue segmented circle around KRHV, before it meets the linear edge of the 700'-floor E5 airspace coming up from the southeast.  So the edge of the 700'-floor E5 "transition area" does indeed run through the blue segmented circle around KRHV much as was sketched in the question.  Area "1" is outside the 700'-floor E5 transition area and has a Class E floor at 1200' AGL when the Class D airspace is inactive, while area "2" is inside the 700'-floor E5 transition area and has a Class E floor at 700' AGL when the Class D airspace is inactive.
This answer has followed the common practice of referring to E5 airspace with a 700' Class E floor as a "transition area".  This appears not to be actually supported by any current FAR or FAA document, including the "Airspace Designations and Reporting Points" document.  "Transition area" is a term from before the 1993 "alphabet" airspace re-organization, and actually included areas that had controlled airspace floors at 1200' AGL as well as at 700' AGL.  It is an obsolete term now, but still is often used by pilots, most commonly to refer to areas that have Class E floors at 700' AGL.  At any rate, note that area "1" is actually still inside the airspace that is defined as part of the E5 airspace associated with San Jose International-- specifically, it is inside the portion of the E5 airspace associated with San Jose International that has a 1200' AGL floor.  This answer does not intend to imply that there is some definitive reason to say that area "2" is inside a "transition area" while area "1" is not inside any "transition area".  The main point of this answer is simply that when the Class D airspace around KRHV is inactive, area "2" has a 700' AGL Class E floor while area "1" has a 1200' AGL Class E floor.
Note that the "Airspace Designations and Reporting Points" document uses nautical miles and true bearings.  A bearing of 139 degrees true is approximately 126 degrees magnetic at this location.

This answer could be completely worked to avoid the use of the phrase "transition area", and substitute the phrase "700'-AGL-floor E5 airspace area" or similar.  Not sure whether that would really be an improvement.

@rvernica -- If I were writing this answer now, I would not use the phrase "it is logical to assume". Similar cases arise with surface-level Class E airspace (shown by a dashed magenta circle rather than a dashed blue circle), and this surface-level Class E airspace is often not in effect 24/7, so again the same question arises. I've found examples of cases where the 700'/1200' boundary continues straight across, as well as cases where it detours to encompass the entire dashed magenta circle, as well as some other more "oddball" cases.

(ctd)  A useful tool to visualize the actual airspace boundaries is the LAANC map. See https://aviation.stackexchange.com/a/97285/34686 for more.

PS. -- in the absence of definite knowledge to the contrary, obviously the most conservative course is to assume that the 700' Class E floor covers the entire Class D airspace, when that Class D airspace is not in effect, and likewise for surface-level Class E airspace.  (At least, that's the most conservative/ restrictive viewpoint from the standpoint of a VFR pilot.  For IFR it may be a different matter.)

The same question re the precise location of the 700'/1200' boundary in areas where it is not clearly depicted on the sectional chart, also arises in relation to Surface-level Class E airspace even during the hours that that Surface-level Class E airspace is actually in effect in relation to some, arguably misguided, interpretations of some FARs such as 103.17.  For more, see https://aviation.stackexchange.com/a/74982/34686, https://aviation.stackexchange.com/a/35331/34686.

The Class E transition area appears to be protecting the IAPs for RWY30L&R of KSJC. So, area #1 would be at 1200 AGL. Area #2 would be at 700 AGL. Considering the MEFs of the surrounding areas range from 3200 MSL to 4800 MSL, it may be a necessary precaution to separate the IFR traffic from the nearby Class G at the surface VFR traffic of E16.

Did you mean 1200' instead of 1500'?

@quietflyer -  Yes, I did. Thanks for the catch.


text:
Does an airfoil drag coefficient takes parasite drag into account?
Im trying to understand why does L/D MAX, (the top of the polar curve that computes CL & CD ratio for any airfoil) is also the lowest point of the total drag curve.
Im guessing the reason is that CD curve is not just about induced drag as I thought.

Airfoil drag is "parasitic" (or better: everything but induced) drag.
It consists of shear drag and pressure drag, the latter mostly from local flow separation. Both are only present when viscous flow is assumed. Airfoil drag is for the wing section without taking tip effects into account, presuming an infinitely wide wing. This kind of theoretical wing has no induced drag (d'Alembert's paradox).
L/D max is the point on the polar curve where the angle to the origin of the coordinate system is steepest. This is not the point of the lowest drag coefficient! Maybe you mean the point of lowest drag for a full airplane – but that is another story, with more than just the airfoil polar. Now induced drag is part of overall drag and due to its inverse relationship with speed, a distinct minimum can be found when lift is held constant.

Drag polar of the NACA 23012 airfoil (picture source, colored comments own work)

I don´t know how to add the graph´s picture I was making reference to (RAF 32 airfoil), sorry about that... but in that one there are two Y axis, (one for CL,the other one for CD and the X axis is for AOA (I thought Cd was all about induced drag because of that). And L/D max is the AOA which correspond to the top of the polar curve (Cl/Cd). What Im trying to understand is how can that airfoil´s L/D max can also be found at the "point of lowest drag for a full airplane" where total drag is at its minimum?

@Cristóbal: When in edit mode, there should be a symbol of a landscape in the toolbar. This lets you add either a link to a picture or upload a picture to add to your text. Did you try the help center yet (symbol with question mark in the top right)?

@ Peter Kampf: I don´t see any landscape symbol when in edit mode. I also cheked help center and I found same instructions about the symbol or link. Unfortunately there is no link to directly see the picture, so Im gonna paste the link of the site where the graph is ,even though I think the graph is not really important to answer my question. Thanks for your help. https://rcplanes.online/design.htm    (Characteristic curves of RAF 32)

I'm trying to understand why does L/D MAX, (the top of the polar curve
that computes CL & CD ratio for any airfoil) is also the lowest point
of the total drag curve.

The graph in another answer shows how to find the max ratio of Cl / Cd, which is arithmetically equal to the max ratio of L/D.
The concept of minimum Drag (as opposed to minimum Drag coefficient) can be confusing.  If we are talking about a Cl vs Cd graph obtained in a wind tunnel with constant airspeed, whether for an airfoil or for a whole airplane, we could say that Drag is minimized when Cd is minimized.  This is obviously not the point where the Cl / Cd ratio is maximized.
But the situation is completely different in actual flight, where Lift is constrained to be equal to Weight (or in the case of a steady-state glide, constrained to be equal to Weight * cos ((arctan (D/L))), which is nearly equal to Weight), and the airspeed varies accordingly. In this case, we can show that Drag is minimized when the L/D (and Cl / Cd ) ratio is maximized, even though this is not the point where the Drag coefficient is smallest.
In the context of actual flight, we need to talk about the L/D or Cl / Cd ratio of the whole aircraft.  Therefore there's really no context in which it makes sense to say that Drag is minimized when the Cl / Cd ratio of the airfoil is maximized.
Related ASE links--
Can we show through simple geometry rather than formulae or graphs that the best glide ratio occurs at the maximum ratio of Lift to Drag?

Airfol´s graph LDmax shows an AOA, and total drag curve´s LDmax shows a TAS. And I was thinking that flying leveled at that shown TAS would adjust that AOA for LDmax. But ...isn´t there a relationship between these two? Is L/D max just a concept that can be used for describing the best Lift-drag ratio of different things without any relationship?


text:
Does a class E airspace still exist when the associated control tower is closed?
An airport tower closes at 1600 hours:

Does the extension (class E from surface up) airspace becomes non existing?
Can I fly through since the tower is closed?

Maybe, when it says "closes at 1600 hours", is that local time, or UTC? Have you read the AF/D (now called the Chart Supplement)? It may be E or G depending on what the CS says.

It depends on the jurisdiction.

Let me add a little more info. This is a helicopter manufacturing plant (Sikorsky ).. When the tower closes ,all flying is suspended. It's a class D airport with the E extension.  Closes at local time.

Welcome to aviation.SE! Which country or regulations are you asking about? And if you have a specific airport as an example, please tell us which one it is. It's best to edit your question to add new information.

In the US, what happens to airspace when the Tower is closed can also depend on the weather reporting available -- typically E if there is an AWOS/ASOS, G otherwise. But I don't think this is a rule, always check the A/FD.

@quietflyer almost certainly https://www.airnav.com/airport/06FA

Re my 3-20-2022 edit of Q- ok, maybe he really did mean when the AIRPORT is closed, in the title-- but since that was only clear from a comment, not from the question, and since the question and title ought to match, I'll refrain from rolling it back. If someone wants to also know what happens when the airport is closed they could add another part to the question, or ask a new one. Plus, it's not really clear that the airport is actually closed when the tower is closed--if the above airport suggestion is correct, AIRNAV page says "WHEN ATCT CLSD, FOR CD CTC PALM BEACH APCH AT 561-275-1430"

Does the extension (class E from surface up) airspace becomes non
existing?

It depends on whether the Class D airspace at the surface reverts to surface-level Class E airspace, or to Class G airspace (usually with a Class E floor above, at 700' AGL or 1200' AGL), when the tower closes.
If the Class D converts to surface-level Class E airspace, then the extensions remain in place as surface-level Class E airspace.
If the Class D converts to Class G (usually with a Class E floor above, at 700' AGL or 1200' AGL), so do the extensions.
This is clarified by the following content in the "Airspace" entry in the "Legend" section of the "Chart Supplement" (formerly "Airport/Facilities Directory") :

NOTE: AIRSPACE SVC "TIMES" INCLUDE ALL ASSOCIATED ARRIVAL EXTENSIONS.
Surface area arrival extensions for instrument approaches become part
of the primary core surface area.  These extensions may be be either
Class D or Class E airspace and are effective concurrent with the time
of the primary core surface area.  For example, when a part-time Class
C, Class D, or Class E surface area defaults to Class G, the
associated arrival extensions will default to Class E at the same
time.   When a part-time Class C or Class D surface area defaults to
Class E, the arrival extensions will remain in effect as Class E
airspace.

The full content of the "Airspace" entry (item 30, on the page labelled p.26) in the "Legend" section of the Chart Supplement (Northeast region, issue effective beginning 3-24-2022) is attached below.
In the case where the Class D converts to Class G and the "extensions" therefore vanish, be aware that there is some slightly misleading content in the Legend of the Chart Supplement-- the Legend indicates that the actual Airspace entries for each airport also clarify whether the overlying Class E airspace begins at 700' or 1200' AGL, but that's not really true.  You have to figure that out by looking at the sectional chart.
At any rate, you won't have any trouble telling from the Chart Supplement whether the core Class D airspace converts to surface-level Class E airspace (and the "extensions" therefore remain), or converts to Class G airspace (and the "extensions" therefore vanish.)
You should be able to tell the same information from the sectional chart itself.  ***(Caution: this only works for airports that do have surface-level Class E extensions, not for those that lack surface-level Class E extensions.)  Here's how the system is supposed to work:
If the Class D airspace reverts all the way to Class G, then the sectional chart is supposed to depict that there is a change in status of the core Class D airspace and the surface-level Class E extensions.  Because both are reverting to Class G.  This is accomplished via the use of the phrase "See Chart Supplement for D/E(surf) eff hrs".
If the Class D airspace reverts to surface-level Class E airspace, then the sectional chart is supposed to depict that there is a change only in the status of the core Class D airspace.  Because the status of the "extensions" is not changing.  This is accomplished via the use of the phrase "See Chart Supplement for D eff hrs".
(For airports where are no surface-level Class E "extensions" to the Class D airspace, the latter phrase is always used, hence the word of caution. In this case the use of this phrase on the sectional chart must not be taken as an indication that the Class D airspace reverts to surface-level Class E airspace, rather than Class G airspace, when the tower is closed.  Instead, the pilot must consult the Chart Supplement.)
There have been some errors in the past when this system was not uniformly adopted, and the former phrase on the sectional chart was incorrectly applied to cases where the Class D airspace reverted to surface-level Class E airspace (and the "extensions" therefore remained as surface-level Class E airspace).1  Some of these inconsistencies would certainly have been present at the time that the question was originally asked.  Most or all of these cases have apparently been recently corrected.2  In all cases, the Chart Supplement itself did correctly explain the status of the airspace.

Can I fly through since the tower is closed?

You don't normally need to talk to anyone to fly through Class E airspace -- including the surface-level Class E "extensions", or the core surface-level Class E airspace areas that actually include the airports for which they are designated -- unless you can't maintain the relevant VFR cloud clearance and visibility requirements, in which case you might consider requesting a Special VFR clearance.  Note that FAR 91.155(c) prohibits operation below a cloud ceiling that is lower than 1000' AGL in Class E airspace that extends all the way down to ground level, unless you obtain a Special VFR clearance.  (There is actually some ambiguity around whether or not Special VFR clearance would even be valid for a surface-level Class E "extension".  For more on this, see the links near the end of this related ASE answer.)

Footnotes:
1,2) See ACM Charting Group Minutes here -- https://www.faa.gov/air_traffic/flight_info/aeronav/acf/media/RDs/21-01-360_Contolled_Airspace_Effective_Hours.pdf .  See also this related ASE answer.

Re "Most or of all of these cases have apparently recently been corrected"-- near superscript "2" -- actually, KNHK and KNTU still have the faulty notation on the sectional chart, reading "See NOTAMs/Supplement for Class D/E (sfc) eff hrs", even though their airspace is actually in effect 24/7. Latest chart checked: Washington sectional chart effective beginning March 24 2022.  But I now understand that this is scheduled to be corrected in the sectional chart effective beginning May 19 2022.

Might be more clear to say -- "including the surface-level Class E "extensions", AS WELL as the core surface-level Class E airspace areas that actually include the airports for which they are designated -- ..."

Triple asterisks visible in answer were supposed to be formatting indications and should be deleted

Link in long string of of underlined (linking) text beginning with "slightly misleading content..." links to wrong ASE answer.  Supposed to go here: https://aviation.stackexchange.com/q/86583/34686